×

Periodic cohomology and free and proper actions on \(\mathbb{R}^n\times S^m\). (English) Zbl 1007.20052

Campbell, C. M. (ed.) et al., Groups St. Andrews 1997 in Bath. Selected papers of the international conference, Bath, UK, July 26-August 9, 1997. Vol. 2. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 261, 701-717 (1999).
This paper is structured in four sections. The first three of them give a brief survey about periodicity in Tate cohomology of finite groups, periodicity in the cohomology after some steps and generalized Tate cohomologies. In the last section it is obtained the main result: If a countable group \(G\) has periodic cohomology after 1-step then \(G\) acts freely and properly on \(\mathbb{R}^n\times S^m\), for some \(n\) and \(m\). – It is useful to mention that at the end of the paper there are given some very interesting conjectures.
For the entire collection see [Zbl 0908.00018].

MSC:

20J06 Cohomology of groups
57M60 Group actions on manifolds and cell complexes in low dimensions
57S25 Groups acting on specific manifolds
57S30 Discontinuous groups of transformations
PDFBibTeX XMLCite